%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : GRP645+4 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 12:44:32 PM UTC 2026
% Result : Theorem 175.12s 29.99s
% Output : CNFRefutation 175.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 9
% Syntax : Number of formulae : 61 ( 22 unt; 0 def)
% Number of atoms : 353 ( 31 equ)
% Maximal formula atoms : 38 ( 5 avg)
% Number of connectives : 446 ( 154 ~; 156 |; 95 &)
% ( 4 <=>; 37 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 3 con; 0-3 aty)
% Number of variables : 99 ( 0 sgn 70 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t24_latsubgr,conjecture,
! [X1] :
( ( l1_group_1(X1)
& v4_group_1(X1)
& v3_group_1(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( ( m1_group_2(X2,X1)
& v1_group_1(X2) )
=> ! [X3] :
( ( m1_group_2(X3,X1)
& v1_group_1(X3) )
=> k1_funct_1(k1_latsubgr(X1),k9_group_2(X1,X2,X3)) = k3_xboole_0(k1_funct_1(k1_latsubgr(X1),X2),k1_funct_1(k1_latsubgr(X1),X3)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_latsubgr) ).
fof(t106_group_2,axiom,
! [X1] :
( ( l1_group_1(X1)
& v4_group_1(X1)
& v3_group_1(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( m1_group_2(X2,X1)
=> ! [X3] :
( m1_group_2(X3,X1)
=> ( m1_group_2(k9_group_2(X1,X2,X3),X3)
& m1_group_2(k9_group_2(X1,X2,X3),X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+246.ax',t106_group_2) ).
fof(redefinition_m1_group_6,axiom,
! [X1,X2] :
( ( m1_group_2(X2,X1)
& l1_group_1(X1)
& v4_group_1(X1)
& v3_group_1(X1)
& ~ v3_struct_0(X1) )
=> ! [X3] :
( m1_group_6(X3,X1,X2)
<=> m1_group_2(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+312.ax',redefinition_m1_group_6) ).
fof(d1_latsubgr,axiom,
! [X1] :
( ( l1_group_1(X1)
& v4_group_1(X1)
& v3_group_1(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( ( m2_relset_1(X2,k1_group_3(X1),k1_zfmisc_1(u1_struct_0(X1)))
& v1_funct_2(X2,k1_group_3(X1),k1_zfmisc_1(u1_struct_0(X1)))
& v1_funct_1(X2) )
=> ( X2 = k1_latsubgr(X1)
<=> ! [X3] :
( ( m1_group_2(X3,X1)
& v1_group_1(X3) )
=> k1_funct_1(X2,X3) = u1_struct_0(X3) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_latsubgr) ).
fof(dt_k1_latsubgr,axiom,
! [X1] :
( ( l1_group_1(X1)
& v4_group_1(X1)
& v3_group_1(X1)
& ~ v3_struct_0(X1) )
=> ( m2_relset_1(k1_latsubgr(X1),k1_group_3(X1),k1_zfmisc_1(u1_struct_0(X1)))
& v1_funct_2(k1_latsubgr(X1),k1_group_3(X1),k1_zfmisc_1(u1_struct_0(X1)))
& v1_funct_1(k1_latsubgr(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_latsubgr) ).
fof(dt_k9_group_2,axiom,
! [X1,X2,X3] :
( ( m1_group_2(X3,X1)
& m1_group_2(X2,X1)
& l1_group_1(X1)
& v4_group_1(X1)
& v3_group_1(X1)
& ~ v3_struct_0(X1) )
=> ( m1_group_2(k9_group_2(X1,X2,X3),X1)
& v1_group_1(k9_group_2(X1,X2,X3)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+246.ax',dt_k9_group_2) ).
fof(dt_m1_group_6,axiom,
! [X1,X2] :
( ( m1_group_2(X2,X1)
& l1_group_1(X1)
& v4_group_1(X1)
& v3_group_1(X1)
& ~ v3_struct_0(X1) )
=> ! [X3] :
( m1_group_6(X3,X1,X2)
=> m1_group_2(X3,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+312.ax',dt_m1_group_6) ).
fof(t1_latsubgr,axiom,
! [X1] :
( ( l1_group_1(X1)
& v4_group_1(X1)
& v3_group_1(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( m1_group_2(X2,X1)
=> ! [X3] :
( m1_group_2(X3,X1)
=> u1_struct_0(k9_group_2(X1,X2,X3)) = k3_xboole_0(u1_struct_0(X2),u1_struct_0(X3)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_latsubgr) ).
fof(commutativity_k3_xboole_0,axiom,
! [X1,X2] : k3_xboole_0(X1,X2) = k3_xboole_0(X2,X1),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+2.ax',commutativity_k3_xboole_0) ).
fof(c_0_9,negated_conjecture,
~ ! [X1] :
( ( l1_group_1(X1)
& v4_group_1(X1)
& v3_group_1(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( ( m1_group_2(X2,X1)
& v1_group_1(X2) )
=> ! [X3] :
( ( m1_group_2(X3,X1)
& v1_group_1(X3) )
=> k1_funct_1(k1_latsubgr(X1),k9_group_2(X1,X2,X3)) = k3_xboole_0(k1_funct_1(k1_latsubgr(X1),X2),k1_funct_1(k1_latsubgr(X1),X3)) ) ) ),
inference(assume_negation,[status(cth)],[t24_latsubgr]) ).
fof(c_0_10,plain,
! [X1] :
( ( l1_group_1(X1)
& v4_group_1(X1)
& v3_group_1(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( m1_group_2(X2,X1)
=> ! [X3] :
( m1_group_2(X3,X1)
=> ( m1_group_2(k9_group_2(X1,X2,X3),X3)
& m1_group_2(k9_group_2(X1,X2,X3),X2) ) ) ) ),
inference(fof_simplification,[status(thm)],[t106_group_2]) ).
fof(c_0_11,negated_conjecture,
~ ! [X1] :
( ( l1_group_1(X1)
& v4_group_1(X1)
& v3_group_1(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( ( m1_group_2(X2,X1)
& v1_group_1(X2) )
=> ! [X3] :
( ( m1_group_2(X3,X1)
& v1_group_1(X3) )
=> k1_funct_1(k1_latsubgr(X1),k9_group_2(X1,X2,X3)) = k3_xboole_0(k1_funct_1(k1_latsubgr(X1),X2),k1_funct_1(k1_latsubgr(X1),X3)) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_9]) ).
fof(c_0_12,plain,
! [X1,X2] :
( ( m1_group_2(X2,X1)
& l1_group_1(X1)
& v4_group_1(X1)
& v3_group_1(X1)
& ~ v3_struct_0(X1) )
=> ! [X3] :
( m1_group_6(X3,X1,X2)
<=> m1_group_2(X3,X2) ) ),
inference(fof_simplification,[status(thm)],[redefinition_m1_group_6]) ).
fof(c_0_13,plain,
! [X344,X345,X346] :
( ( ~ l1_group_1(X344)
| ~ v4_group_1(X344)
| ~ v3_group_1(X344)
| v3_struct_0(X344)
| ~ m1_group_2(X345,X344)
| ~ m1_group_2(X346,X344)
| m1_group_2(k9_group_2(X344,X345,X346),X346) )
& ( ~ l1_group_1(X344)
| ~ v4_group_1(X344)
| ~ v3_group_1(X344)
| v3_struct_0(X344)
| ~ m1_group_2(X345,X344)
| ~ m1_group_2(X346,X344)
| m1_group_2(k9_group_2(X344,X345,X346),X345) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])])])]) ).
fof(c_0_14,negated_conjecture,
( k1_funct_1(k1_latsubgr(esk1_0),k9_group_2(esk1_0,esk2_0,esk3_0)) != k3_xboole_0(k1_funct_1(k1_latsubgr(esk1_0),esk2_0),k1_funct_1(k1_latsubgr(esk1_0),esk3_0))
& m1_group_2(esk3_0,esk1_0)
& v1_group_1(esk3_0)
& m1_group_2(esk2_0,esk1_0)
& v1_group_1(esk2_0)
& l1_group_1(esk1_0)
& v4_group_1(esk1_0)
& v3_group_1(esk1_0)
& ~ v3_struct_0(esk1_0) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])])]) ).
fof(c_0_15,plain,
! [X1] :
( ( l1_group_1(X1)
& v4_group_1(X1)
& v3_group_1(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( ( m2_relset_1(X2,k1_group_3(X1),k1_zfmisc_1(u1_struct_0(X1)))
& v1_funct_2(X2,k1_group_3(X1),k1_zfmisc_1(u1_struct_0(X1)))
& v1_funct_1(X2) )
=> ( X2 = k1_latsubgr(X1)
<=> ! [X3] :
( ( m1_group_2(X3,X1)
& v1_group_1(X3) )
=> k1_funct_1(X2,X3) = u1_struct_0(X3) ) ) ) ),
inference(fof_simplification,[status(thm)],[d1_latsubgr]) ).
fof(c_0_16,plain,
! [X1] :
( ( l1_group_1(X1)
& v4_group_1(X1)
& v3_group_1(X1)
& ~ v3_struct_0(X1) )
=> ( m2_relset_1(k1_latsubgr(X1),k1_group_3(X1),k1_zfmisc_1(u1_struct_0(X1)))
& v1_funct_2(k1_latsubgr(X1),k1_group_3(X1),k1_zfmisc_1(u1_struct_0(X1)))
& v1_funct_1(k1_latsubgr(X1)) ) ),
inference(fof_simplification,[status(thm)],[dt_k1_latsubgr]) ).
fof(c_0_17,plain,
! [X2808,X2809,X2810] :
( ( ~ m1_group_2(X2809,X2808)
| ~ l1_group_1(X2808)
| ~ v4_group_1(X2808)
| ~ v3_group_1(X2808)
| v3_struct_0(X2808)
| m1_group_6(X2810,X2808,X2809)
| ~ m1_group_2(X2810,X2809) )
& ( ~ m1_group_2(X2809,X2808)
| ~ l1_group_1(X2808)
| ~ v4_group_1(X2808)
| ~ v3_group_1(X2808)
| v3_struct_0(X2808)
| m1_group_2(X2810,X2809)
| ~ m1_group_6(X2810,X2808,X2809) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])])])])]) ).
cnf(c_0_18,plain,
( ~ l1_group_1(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1)
| ~ m1_group_2(X2,X1)
| ~ m1_group_2(X3,X1)
| v3_struct_0(X1)
| m1_group_2(k9_group_2(X1,X2,X3),X3) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_19,negated_conjecture,
m1_group_2(esk3_0,esk1_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_20,negated_conjecture,
v4_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_21,negated_conjecture,
v3_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_22,negated_conjecture,
l1_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_23,negated_conjecture,
~ v3_struct_0(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
fof(c_0_24,plain,
! [X1,X2,X3] :
( ( m1_group_2(X3,X1)
& m1_group_2(X2,X1)
& l1_group_1(X1)
& v4_group_1(X1)
& v3_group_1(X1)
& ~ v3_struct_0(X1) )
=> ( m1_group_2(k9_group_2(X1,X2,X3),X1)
& v1_group_1(k9_group_2(X1,X2,X3)) ) ),
inference(fof_simplification,[status(thm)],[dt_k9_group_2]) ).
fof(c_0_25,plain,
! [X314,X315,X316] :
( ( ~ l1_group_1(X314)
| ~ v4_group_1(X314)
| ~ v3_group_1(X314)
| v3_struct_0(X314)
| ~ m2_relset_1(X315,k1_group_3(X314),k1_zfmisc_1(u1_struct_0(X314)))
| ~ v1_funct_2(X315,k1_group_3(X314),k1_zfmisc_1(u1_struct_0(X314)))
| ~ v1_funct_1(X315)
| X315 = k1_latsubgr(X314)
| k1_funct_1(X315,esk28_2(X314,X315)) != u1_struct_0(esk28_2(X314,X315)) )
& ( ~ l1_group_1(X314)
| ~ v4_group_1(X314)
| ~ v3_group_1(X314)
| v3_struct_0(X314)
| ~ m2_relset_1(X315,k1_group_3(X314),k1_zfmisc_1(u1_struct_0(X314)))
| ~ v1_funct_2(X315,k1_group_3(X314),k1_zfmisc_1(u1_struct_0(X314)))
| ~ v1_funct_1(X315)
| X315 = k1_latsubgr(X314)
| m1_group_2(esk28_2(X314,X315),X314) )
& ( ~ l1_group_1(X314)
| ~ v4_group_1(X314)
| ~ v3_group_1(X314)
| v3_struct_0(X314)
| ~ m2_relset_1(X315,k1_group_3(X314),k1_zfmisc_1(u1_struct_0(X314)))
| ~ v1_funct_2(X315,k1_group_3(X314),k1_zfmisc_1(u1_struct_0(X314)))
| ~ v1_funct_1(X315)
| X315 = k1_latsubgr(X314)
| v1_group_1(esk28_2(X314,X315)) )
& ( ~ l1_group_1(X314)
| ~ v4_group_1(X314)
| ~ v3_group_1(X314)
| v3_struct_0(X314)
| ~ m2_relset_1(X315,k1_group_3(X314),k1_zfmisc_1(u1_struct_0(X314)))
| ~ v1_funct_2(X315,k1_group_3(X314),k1_zfmisc_1(u1_struct_0(X314)))
| ~ v1_funct_1(X315)
| k1_funct_1(X315,X316) = u1_struct_0(X316)
| ~ m1_group_2(X316,X314)
| ~ v1_group_1(X316)
| X315 != k1_latsubgr(X314) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_15])])])])])]) ).
fof(c_0_26,plain,
! [X313] :
( ( ~ l1_group_1(X313)
| ~ v4_group_1(X313)
| ~ v3_group_1(X313)
| v3_struct_0(X313)
| m2_relset_1(k1_latsubgr(X313),k1_group_3(X313),k1_zfmisc_1(u1_struct_0(X313))) )
& ( ~ l1_group_1(X313)
| ~ v4_group_1(X313)
| ~ v3_group_1(X313)
| v3_struct_0(X313)
| v1_funct_2(k1_latsubgr(X313),k1_group_3(X313),k1_zfmisc_1(u1_struct_0(X313))) )
& ( ~ l1_group_1(X313)
| ~ v4_group_1(X313)
| ~ v3_group_1(X313)
| v3_struct_0(X313)
| v1_funct_1(k1_latsubgr(X313)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_16])])])]) ).
fof(c_0_27,plain,
! [X1,X2] :
( ( m1_group_2(X2,X1)
& l1_group_1(X1)
& v4_group_1(X1)
& v3_group_1(X1)
& ~ v3_struct_0(X1) )
=> ! [X3] :
( m1_group_6(X3,X1,X2)
=> m1_group_2(X3,X1) ) ),
inference(fof_simplification,[status(thm)],[dt_m1_group_6]) ).
cnf(c_0_28,plain,
( ~ m1_group_2(X2,X3)
| ~ l1_group_1(X3)
| ~ v4_group_1(X3)
| ~ v3_group_1(X3)
| ~ m1_group_2(X1,X2)
| v3_struct_0(X3)
| m1_group_6(X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_29,negated_conjecture,
( ~ m1_group_2(X1,esk1_0)
| m1_group_2(k9_group_2(esk1_0,X1,esk3_0),esk3_0) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20]),c_0_21]),c_0_22])]),c_0_23]) ).
cnf(c_0_30,negated_conjecture,
m1_group_2(esk2_0,esk1_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
fof(c_0_31,plain,
! [X365,X366,X367] :
( ( ~ m1_group_2(X367,X365)
| ~ m1_group_2(X366,X365)
| ~ l1_group_1(X365)
| ~ v4_group_1(X365)
| ~ v3_group_1(X365)
| v3_struct_0(X365)
| m1_group_2(k9_group_2(X365,X366,X367),X365) )
& ( ~ m1_group_2(X367,X365)
| ~ m1_group_2(X366,X365)
| ~ l1_group_1(X365)
| ~ v4_group_1(X365)
| ~ v3_group_1(X365)
| v3_struct_0(X365)
| v1_group_1(k9_group_2(X365,X366,X367)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_24])])])]) ).
cnf(c_0_32,plain,
( ~ l1_group_1(X2)
| ~ v4_group_1(X2)
| ~ v3_group_1(X2)
| ~ m2_relset_1(X1,k1_group_3(X2),k1_zfmisc_1(u1_struct_0(X2)))
| ~ v1_funct_2(X1,k1_group_3(X2),k1_zfmisc_1(u1_struct_0(X2)))
| ~ v1_funct_1(X1)
| ~ m1_group_2(X3,X2)
| ~ v1_group_1(X3)
| X1 != k1_latsubgr(X2)
| v3_struct_0(X2)
| k1_funct_1(X1,X3) = u1_struct_0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_33,plain,
( ~ l1_group_1(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1)
| v3_struct_0(X1)
| v1_funct_1(k1_latsubgr(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_34,plain,
( ~ l1_group_1(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1)
| v3_struct_0(X1)
| m2_relset_1(k1_latsubgr(X1),k1_group_3(X1),k1_zfmisc_1(u1_struct_0(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_35,plain,
( ~ l1_group_1(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1)
| v3_struct_0(X1)
| v1_funct_2(k1_latsubgr(X1),k1_group_3(X1),k1_zfmisc_1(u1_struct_0(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
fof(c_0_36,plain,
! [X2802,X2803,X2804] :
( m1_group_2(X2804,X2802)
| ~ m1_group_6(X2804,X2802,X2803)
| ~ m1_group_2(X2803,X2802)
| ~ l1_group_1(X2802)
| ~ v4_group_1(X2802)
| ~ v3_group_1(X2802)
| v3_struct_0(X2802) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_27])])])]) ).
cnf(c_0_37,negated_conjecture,
( ~ m1_group_2(X1,esk3_0)
| m1_group_6(X1,esk1_0,esk3_0) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_19]),c_0_20]),c_0_21]),c_0_22])]),c_0_23]) ).
cnf(c_0_38,negated_conjecture,
m1_group_2(k9_group_2(esk1_0,esk2_0,esk3_0),esk3_0),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_39,plain,
( ~ m1_group_2(X3,X1)
| ~ m1_group_2(X2,X1)
| ~ l1_group_1(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1)
| v3_struct_0(X1)
| v1_group_1(k9_group_2(X1,X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
fof(c_0_40,plain,
! [X1] :
( ( l1_group_1(X1)
& v4_group_1(X1)
& v3_group_1(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( m1_group_2(X2,X1)
=> ! [X3] :
( m1_group_2(X3,X1)
=> u1_struct_0(k9_group_2(X1,X2,X3)) = k3_xboole_0(u1_struct_0(X2),u1_struct_0(X3)) ) ) ),
inference(fof_simplification,[status(thm)],[t1_latsubgr]) ).
cnf(c_0_41,plain,
( ~ l1_group_1(X1)
| ~ v1_group_1(X2)
| ~ v3_group_1(X1)
| ~ v4_group_1(X1)
| ~ m1_group_2(X2,X1)
| v3_struct_0(X1)
| k1_funct_1(k1_latsubgr(X1),X2) = u1_struct_0(X2) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_32]),c_0_33]),c_0_34]),c_0_35]) ).
cnf(c_0_42,negated_conjecture,
v1_group_1(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
fof(c_0_43,plain,
! [X72,X73] : k3_xboole_0(X72,X73) = k3_xboole_0(X73,X72),
inference(variable_rename,[status(thm)],[commutativity_k3_xboole_0]) ).
cnf(c_0_44,negated_conjecture,
v1_group_1(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_45,plain,
( ~ m1_group_6(X3,X1,X2)
| ~ m1_group_2(X2,X1)
| ~ l1_group_1(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1)
| m1_group_2(X3,X1)
| v3_struct_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_46,negated_conjecture,
m1_group_6(k9_group_2(esk1_0,esk2_0,esk3_0),esk1_0,esk3_0),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_47,negated_conjecture,
( ~ m1_group_2(X1,esk1_0)
| v1_group_1(k9_group_2(esk1_0,X1,esk3_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_19]),c_0_20]),c_0_21]),c_0_22])]),c_0_23]) ).
fof(c_0_48,plain,
! [X404,X405,X406] :
( u1_struct_0(k9_group_2(X404,X405,X406)) = k3_xboole_0(u1_struct_0(X405),u1_struct_0(X406))
| ~ m1_group_2(X406,X404)
| ~ m1_group_2(X405,X404)
| ~ l1_group_1(X404)
| ~ v4_group_1(X404)
| ~ v3_group_1(X404)
| v3_struct_0(X404) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_40])])])]) ).
cnf(c_0_49,negated_conjecture,
k1_funct_1(k1_latsubgr(esk1_0),k9_group_2(esk1_0,esk2_0,esk3_0)) != k3_xboole_0(k1_funct_1(k1_latsubgr(esk1_0),esk2_0),k1_funct_1(k1_latsubgr(esk1_0),esk3_0)),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_50,negated_conjecture,
k1_funct_1(k1_latsubgr(esk1_0),esk3_0) = u1_struct_0(esk3_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_19]),c_0_20]),c_0_21]),c_0_42]),c_0_22])]),c_0_23]) ).
cnf(c_0_51,plain,
k3_xboole_0(X1,X2) = k3_xboole_0(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_52,negated_conjecture,
k1_funct_1(k1_latsubgr(esk1_0),esk2_0) = u1_struct_0(esk2_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_30]),c_0_20]),c_0_21]),c_0_44]),c_0_22])]),c_0_23]) ).
cnf(c_0_53,negated_conjecture,
m1_group_2(k9_group_2(esk1_0,esk2_0,esk3_0),esk1_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_19]),c_0_20]),c_0_21]),c_0_22])]),c_0_23]) ).
cnf(c_0_54,negated_conjecture,
v1_group_1(k9_group_2(esk1_0,esk2_0,esk3_0)),
inference(spm,[status(thm)],[c_0_47,c_0_30]) ).
cnf(c_0_55,plain,
( ~ m1_group_2(X3,X1)
| ~ m1_group_2(X2,X1)
| ~ l1_group_1(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1)
| u1_struct_0(k9_group_2(X1,X2,X3)) = k3_xboole_0(u1_struct_0(X2),u1_struct_0(X3))
| v3_struct_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_56,negated_conjecture,
k1_funct_1(k1_latsubgr(esk1_0),k9_group_2(esk1_0,esk2_0,esk3_0)) != k3_xboole_0(u1_struct_0(esk2_0),u1_struct_0(esk3_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_49,c_0_50]),c_0_51]),c_0_52]),c_0_51]) ).
cnf(c_0_57,negated_conjecture,
k1_funct_1(k1_latsubgr(esk1_0),k9_group_2(esk1_0,esk2_0,esk3_0)) = u1_struct_0(k9_group_2(esk1_0,esk2_0,esk3_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_53]),c_0_20]),c_0_21]),c_0_54]),c_0_22])]),c_0_23]) ).
cnf(c_0_58,negated_conjecture,
( ~ m1_group_2(X1,esk1_0)
| u1_struct_0(k9_group_2(esk1_0,X1,esk3_0)) = k3_xboole_0(u1_struct_0(X1),u1_struct_0(esk3_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_19]),c_0_20]),c_0_21]),c_0_22])]),c_0_23]) ).
cnf(c_0_59,negated_conjecture,
u1_struct_0(k9_group_2(esk1_0,esk2_0,esk3_0)) != k3_xboole_0(u1_struct_0(esk2_0),u1_struct_0(esk3_0)),
inference(rw,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_60,plain,
$false,
inference(cdclpropres,[status(thm)],[c_0_58,c_0_59,c_0_30]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP645+4 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.17/0.43 % Computer : n015.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Sun Sep 20 20:29:05 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.43 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.17/0.50 Running first-order theorem proving
% 0.17/0.51 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 175.12/29.99 % Version: 3.5.1
% 175.12/29.99 % Preprocessing class: FMLLMLLLSSSNFFN.
% 175.12/29.99 % Scheduled 4 strats onto 8 cores with 297 seconds (2376 total)
% 175.12/29.99 % Starting new_bool_3 with 891s (3) cores
% 175.12/29.99 % Starting new_bool_1 with 891s (3) cores
% 175.12/29.99 % Starting sh5l with 297s (1) cores
% 175.12/29.99 % Starting G-E--_207_C01_F1_SE_CS_SP_PI_S5PRR_S0Y with 297s (1) cores
% 175.12/29.99 % new_bool_3 with pid 3875447 completed with status 0
% 175.12/29.99 % Result found by new_bool_3
% 175.12/29.99 % Preprocessing class: FMLLMLLLSSSNFFN.
% 175.12/29.99 % Scheduled 4 strats onto 8 cores with 297 seconds (2376 total)
% 175.12/29.99 % Starting new_bool_3 with 891s (3) cores
% 175.12/29.99 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 175.12/29.99 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 175.12/29.99 % Search class: FGHSM-SMLM32-DFFFFFNN
% 175.12/29.99 % Scheduled 13 strats onto 3 cores with 890 seconds (890 total)
% 175.12/29.99 % Starting SubtermCWHack with 81s (1) cores
% 175.12/29.99 % Starting new_bool_3 with 90s (1) cores
% 175.12/29.99 % Starting G-E--_008_C45_F1_PI_SE_Q4_CS_SP_S4SI with 67s (1) cores
% 175.12/29.99 % new_bool_3 with pid 3875456 completed with status 0
% 175.12/29.99 % Result found by new_bool_3
% 175.12/29.99 % Preprocessing class: FMLLMLLLSSSNFFN.
% 175.12/29.99 % Scheduled 4 strats onto 8 cores with 297 seconds (2376 total)
% 175.12/29.99 % Starting new_bool_3 with 891s (3) cores
% 175.12/29.99 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 175.12/29.99 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 175.12/29.99 % Search class: FGHSM-SMLM32-DFFFFFNN
% 175.12/29.99 % Scheduled 13 strats onto 3 cores with 890 seconds (890 total)
% 175.12/29.99 % Starting SubtermCWHack with 81s (1) cores
% 175.12/29.99 % Starting new_bool_3 with 90s (1) cores
% 175.12/29.99 % Preprocessing time : 0.157 s
% 175.12/29.99 % Presaturation interreduction done
% 175.12/29.99 % SatCheck found unsatisfiable ground set
% 175.12/29.99
% 175.12/29.99 % Proof found!
% 175.12/29.99 % SZS status Theorem
% 175.12/29.99 % SZS output start CNFRefutation
% See solution above
% 175.12/30.00 % Parsed axioms : 36514
% 175.12/30.00 % Removed by relevancy pruning/SinE : 34394
% 175.12/30.00 % Initial clauses : 4390
% 175.12/30.00 % Removed in clause preprocessing : 136
% 175.12/30.00 % Initial clauses in saturation : 4254
% 175.12/30.00 % Processed clauses : 39503
% 175.12/30.00 % ...of these trivial : 2257
% 175.12/30.00 % ...subsumed : 17246
% 175.12/30.00 % ...remaining for further processing : 20000
% 175.12/30.00 % Other redundant clauses eliminated : 2908
% 175.12/30.00 % Clauses deleted for lack of memory : 0
% 175.12/30.00 % Backward-subsumed : 191
% 175.12/30.00 % Backward-rewritten : 424
% 175.12/30.00 % Generated clauses : 505742
% 175.12/30.00 % ...of the previous two non-redundant : 482078
% 175.12/30.00 % ...aggressively subsumed : 0
% 175.12/30.00 % Contextual simplify-reflections : 272
% 175.12/30.00 % Paramodulations : 502627
% 175.12/30.00 % Factorizations : 36
% 175.12/30.00 % NegExts : 0
% 175.12/30.00 % Equation resolutions : 3013
% 175.12/30.00 % Disequality decompositions : 0
% 175.12/30.00 % Total rewrite steps : 952481
% 175.12/30.00 % ...of those cached : 944107
% 175.12/30.00 % Propositional unsat checks : 4
% 175.12/30.00 % Propositional check models : 1
% 175.12/30.00 % Propositional check unsatisfiable : 1
% 175.12/30.00 % Propositional clauses : 465577
% 175.12/30.00 % Propositional clauses after purity: 17043
% 175.12/30.00 % Propositional unsat core size : 3
% 175.12/30.00 % Propositional preprocessing time : 0.000
% 175.12/30.00 % Propositional encoding time : 1.524
% 175.12/30.00 % Propositional solver time : 0.679
% 175.12/30.00 % Success case prop preproc time : 0.000
% 175.12/30.00 % Success case prop encoding time : 1.070
% 175.12/30.00 % Success case prop solver time : 0.124
% 175.12/30.00 % Current number of processed clauses : 15051
% 175.12/30.00 % Positive orientable unit clauses : 7368
% 175.12/30.00 % Positive unorientable unit clauses: 3
% 175.12/30.00 % Negative unit clauses : 2896
% 175.12/30.00 % Non-unit-clauses : 4784
% 175.12/30.00 % Current number of unprocessed clauses: 450526
% 175.12/30.00 % ...number of literals in the above : 1463168
% 175.12/30.00 % Current number of archived formulas : 0
% 175.12/30.00 % Current number of archived clauses : 4650
% 175.12/30.00 % Clause-clause subsumption calls (NU) : 14567145
% 175.12/30.00 % Rec. Clause-clause subsumption calls : 1193079
% 175.12/30.00 % Non-unit clause-clause subsumptions : 1861
% 175.12/30.00 % Unit Clause-clause subsumption calls : 1905030
% 175.12/30.00 % Rewrite failures with RHS unbound : 0
% 175.12/30.00 % BW rewrite match attempts : 733539
% 175.12/30.00 % BW rewrite match successes : 337
% 175.12/30.00 % Condensation attempts : 0
% 175.12/30.00 % Condensation successes : 0
% 175.12/30.00 % Termbank termtop insertions : 21684129
% 175.12/30.00 % Search garbage collected termcells : 434739
% 175.12/30.00
% 175.12/30.00 % -------------------------------------------------
% 175.12/30.00 % User time : 24.282 s
% 175.12/30.00 % System time : 0.859 s
% 175.12/30.00 % Total time : 25.142 s
% 175.12/30.00 % Maximum resident set size: 76704 pages
% 175.12/30.00
% 175.12/30.00 % -------------------------------------------------
% 175.12/30.00 % User time : 72.605 s
% 175.12/30.00 % System time : 2.152 s
% 175.12/30.00 % Total time : 74.756 s
% 175.12/30.00 % Maximum resident set size: 60160 pages
% 175.12/30.00 % E exiting
%------------------------------------------------------------------------------